1) Look at the suppliers that are normally used, some of which are listed below. Mentors usually order parts for students during the hectic 6 week build season. Many of the parts in stock are related to the FIRST FRC supplier site, !AndyMark.com. Once the competition is announced the team gets a "Kit of Parts" for the robot build . It includes dc motors called CIMS (pronounced "sims") as well as competition-specific parts. 

i) !AndyMark.com supplies many of the standard parts for FIRST FRC robotics. You will see substantial overlap between the kit of parts and !AndyMark.com.
ii) Chief Delphi is the site with user forums for FIRST. It is very useful when you want to know what has been tried before and how various challenges are solved.
iii) During the build season you are often limited by the time needed to start shipment. The main quick suppliers are !McMasterCarr.com or Amazon.com. Andymark is slow, but you might be able to get it in two weeks during build season if you order early.

2) Get to know the status of CAD. Many students are learning measurement and fabrication. Producing CAD drawings can generally help students communicate ideas for parts, and can specifically help them specify how to fabricate a part. Although 2537 doesn't rely on it yet, some teams use CAD for the design and integration phase, similar to the professional engineers. This doesn't have to be perfect, but there are plenty of reasons to get it made quickly already. The following programs are available free to students and mentors.

i) Many students learn !AutoDesk Inventor in the high school class "Intro. to Engineering Design." Some learn it well from that class. However, some don't learn it well enough to want to use it again, and others have no CAD experience. This program allows unlimited licenses for educational purposes. It is already installed in the computer lab, although it might be an old version. 
ii) Some teams report that it helps to teach their students a 2D CAD program prior to teaching 3D CAD. We are currently trying out the free 2D CAD program called !DraftSight, and might train students in it.
iii) Solidworks is a popular professional CAD product that is available for free for FIRST FRC. Unfortunately they offer a limited number of licenses. FIRST FRC uses this CAD program to build a virtual robot with control from the same software that be used for a real robot. 

3) Realize that there is no perfect season, but that a good preseason can help students and mentors prepare. In my opinion the mech and other students should learn some physics terminology during this time. To fill the gaps in preseason, Newton's equations with force and unit conversion should be taught in some way. It can help them understand concepts qualitatively, even if they don't use the equations. This is essential for the students so they can effectively have technical discussions later. They need to use these equations quantitatively to work out forces for pistons and motors. In addition, concepts such as precision and accuracy are nice to cover and use, since it is part of the physics (and GRE) curriculum.